Real Hypersurfaces in Complex Two-Plane Grassmannians Whose Jacobi Operators Corresponding to -Directions are of Codazzi Type

We prove the non-existence of Hopf real hypersurfaces in complex two-plane Grassmannians whose Jacobi operators or the Jacobi corresponding to the directions in the distribution are of Codazzi type if they satisfy a further condition. We obtain that that they must be either of type (A) or of type (B) (see [2]), but no one of these satisfies our condition. As a consequence, we obtain the non-existence of Hopf real hypersurfaces in such ambient spaces whose Jacobi operators corresponding to -directions are parallel with the same further condition.

Commuting Structure Jacobi Operator for Real Hypersurfaces in Complex Two-plane Grassmannians

We classify real hypersurfaces in complex two-plane Grassmannians whose structure Jacobi operator commutes either with any other Jacobi operator or with the normal Jacobi operator.

Hopf Hypersurfaces in Complex Two-Plane Grassmannians with Generalized Tanaka–Webster D-Parallel Shape Operator

In this paper, we consider a new notion of generalized Tanaka Webster З-parallel shape operator for a real hypersurface in a complex two-plane Grassrnannian and prove a non-existence theorem of a real hypersurface.

复双平面格拉斯曼中实超曲面的*-Ricci张量

主要考虑在复双曲双面格拉斯曼SU2,m/S(U2U m),m≥2中的实超曲面的复曲率张量中引入*-Ricci张量。我们首先证明了SU2,m/S(U2U m)的Hopf超曲面上不存在*-Einstein度量。作为*-Einstein度量的一个推广,我们引入了*-Ricci孤立子,并证明了一个具有*-Ricci孤立子的实超曲面的位势场是Reeb矢量场,是SU2,m/S(U2U m)中全测地子流行SU2,m-1/S(U2U m-1)管状领域的一部分或者是一个无穷远处的中心是奇异的极限球面。最后,我们研究了一个具有伪反交换*-Ricci张量的Hopf超曲面。